Someone claims that a certain suspension contains at least seven particles per mL. You sample 1 mL of solution. Let X be the number of particles in the sample.

Question

a. If the mean number of partides is exactly seven per mL (so that the claim is true, but just barely), what is P(X ? 1)?
b. Based on the answer to part (a), if the suspension contains seven particles per mL, would one particle in a 1 mL sample be an unusually small number?
c. If you counted one particle in the sample, would this be convincing evidence that the claim is false? Explain.
d. If the mean number of particles is exactly 7 per mL, what is P(X ? 6)?
e. Based on the answer to part (d), if the suspension contains seven particles per mL, would six particles in a 1 mL sample be an unusually small number?
f. If you counted six particles in the sample, would this be convincing evidence that the claim is false? Explain.

Answer 1

If the mean number of particles is exactly 7 per mL, then Poisson



(a)





(b) Yes. If the mean concentration is 7 particles per mL, then only about 7 in every thousand 1 mL samples will

contain 1 or fewer particles.



(c)Yes, because 1 particle in a 1 mL sample is an unusually small number if the mean concentration is 7 particles

per mL.



(d)





(e) No. If the mean concentration is 7 particles per mL, then about 45% of all 1 mL samples will contain 6 or fewer

particles.



(f) No, because 6 particles in a 1 mL sample is not an unusually small number if the mean concentration is 7

particles per mL.